Question

A manufacturer of bicycles builds​ racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 64,600 units of steel and 24, 000 units of aluminum. The​ racing, touring, and mountain models need 17​, 19​, and 34 units of​ steel, and 9​, 21​, and 12 units of​ aluminum, respectively. Complete parts​ (a) through​ (d) below.

a. Set up the Linear Programming problem is x= # of racing bikes, y=# of touring bikes and z = # of mountain bikes

b. How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike, $12 per touring bike, and $22 per mountain bike?

c. What is the maximum possible profit?

d. Are there any units of steel or aluminum leftover? How much?

Answer 1

b. 1,900 mountain bicycles, 0 racing bicycles and 0 touring bicycles to maximize profit

c. $41,800

d. 1,200 units of aluminium is left over

Explanation:

a. Let:

x= Number of racing bikes,

y= Number of touring bikes and

z = Number of mountain bikes

Constraints are;

17x+19y+34z<=64600

9x+21y+12z<=24000

x>=0

y>=0

z>=0

b. Maximize P = 8x+12y+22z

Subject to;

17x+19y+34z<=64600

9x+21y+12z<=24000

with x>=0 ; y>=0 ; z>=0

applying simplex method (see attachment);

z=1900 ; x=0; y=0; P=41,800 ; s₁=0 ; s₂=1200

b. The manufacturer are to make 1,900 mountain bicycles, 0 racing bicycles and 0 touring bicycles to maximize profit

c. Maximum profit is $41,800

d. no steel is leftover while 1,200 units of aluminium is left over.